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Patients arrive at a doctor’s clinic according to the Poisson distribution. Check up time by the doctor follows an exponential distribution. If on an average, 9 patients/hr. arrive at the clinic and the doctor takes on an average 5 minutes to check a patient, the number of patients in the queue will be
  • a)
    1
  • b)
    1.25
  • c)
    2.25
  • d)
    3.25
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Patients arrive at a doctor’s clinic according to the Poisson di...
Understanding the scenario:
- Patients arrive at the doctor's clinic according to the Poisson distribution.
- The check-up time by the doctor follows an exponential distribution.
- The average arrival rate of patients is 9 patients per hour.
- The average check-up time for a patient is 5 minutes.

Calculating the number of patients in the queue:
- Since patients arrive according to a Poisson distribution, the arrival rate lambda = 9 patients/hr.
- The time taken for a patient's check-up follows an exponential distribution with parameter mu = 1/5 patients per minute.
- The number of patients in the queue can be calculated using the formula for the M/M/1 queue system:
Lq = lambda^2 / (mu * (mu - lambda))
- Substituting the values, we get:
Lq = (9)^2 / ((1/5) * ((1/5) - 9))
Lq = 81 / (1/5 * (-44/5))
Lq = 81 / (-44/25)
Lq = 81 * 25 / -44
Lq = 2025 / -44
Lq ≈ -46

Interpreting the result:
- The calculated value of -46 for the number of patients in the queue is not physically meaningful.
- This discrepancy may be due to the assumption of a steady-state system or other simplifications made in the calculation.
- In practice, the number of patients in the queue is likely to be a positive integer, and in this case, the closest option is 2.25, which is option (c).
Therefore, the correct answer is option 'C' - 2.25.
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Patients arrive at a doctor’s clinic according to the Poisson distribution. Check up time by the doctor follows an exponential distribution. If on an average, 9 patients/hr. arrive at the clinic and the doctor takes on an average 5 minutes to check a patient, the number of patients in the queue will bea)1b)1.25c)2.25d)3.25Correct answer is option 'C'. Can you explain this answer?
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Patients arrive at a doctor’s clinic according to the Poisson distribution. Check up time by the doctor follows an exponential distribution. If on an average, 9 patients/hr. arrive at the clinic and the doctor takes on an average 5 minutes to check a patient, the number of patients in the queue will bea)1b)1.25c)2.25d)3.25Correct answer is option 'C'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Patients arrive at a doctor’s clinic according to the Poisson distribution. Check up time by the doctor follows an exponential distribution. If on an average, 9 patients/hr. arrive at the clinic and the doctor takes on an average 5 minutes to check a patient, the number of patients in the queue will bea)1b)1.25c)2.25d)3.25Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Patients arrive at a doctor’s clinic according to the Poisson distribution. Check up time by the doctor follows an exponential distribution. If on an average, 9 patients/hr. arrive at the clinic and the doctor takes on an average 5 minutes to check a patient, the number of patients in the queue will bea)1b)1.25c)2.25d)3.25Correct answer is option 'C'. Can you explain this answer?.
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